Complex Analysis And Applications


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By: Richard A. Book Reg.

Complex Analysis with Applications to Flows and Fields Mathematics and Physics for Science and Techn

Product Description Bonus Editorial Product Details This basic book on functions of a complex variable represents the irreducible minimum of what every scientist and engineer should know about this important subject. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the fundamentals of complex analysis in a concise manner designed not to overwhelm the beginner. The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues.

Abundant exercise material and examples, as well as section-by-section comments at the end of each chapter make this book especially valuable to students and anyone encountering complex analysis for the first time. Reprint of the Prentice-Hall, edition. Richard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the s. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the fundamentals of complex analysis in a concise manner designed not to overwhelm the beginner.

The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues. Abundant exercise material and examples, as well as section-by-section comments at the end of each chapter make this book especially valuable to students and anyone encountering complex analysis for the first time. Reprint of the Prentice-Hall, edition.

Richard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions.

A Collection of Problems on Complex Analysis. In total, we expect that the course will take hours of work per module, depending on your background. Complex analysis is the study of functions that live in the complex plane, that is, functions that have complex arguments and complex outputs. The main goal of this module is to familiarize ourselves with such functions.

This allows us to learn about the basics of the construction of Julia sets of quadratic polynomials. You'll learn everything you need to know to create your own beautiful fractal images, if you so desire.

Complex Analysis

When studying functions we are often interested in their local behavior, more specifically, in how functions change as their argument changes. This leads us to studying complex differentiation — a more powerful concept than that which we learned in calculus. These are functions that possess complex derivatives in lots of places; a fact, which endows them with some of the most beautiful properties mathematics has to offer.

These functions agree with their well-known real-valued counterparts on the real axis! We'll finish this module with the famous and stunning Riemann mapping theorem.


  1. Systems of Linear Inequalities (Little Mathematics Library);
  2. Complex Analysis and Its Applications;
  3. Product Review;
  4. You are here.
  5. Table of contents.
  6. Introduction to Complex Numbers.

This theorem allows us to study arbitrary simply connected sub-regions of the complex plane by transporting geometry and complex analysis from the unit disk to those domains via conformal mappings, the existence of which is guaranteed via the Riemann Mapping Theorem. Now that we are familiar with complex differentiation and analytic functions we are ready to tackle integration. It's going to be a week filled with many amazing results! Power series are especially easy to understand, well behaved and easy to work with. Laurent series are a powerful tool to understand analytic functions near their singularities.

Whereas power series with non-negative exponents can be used to represent analytic functions in disks, Laurent series which can have negative exponents serve a similar purpose in annuli.

MATH - Complex Analysis and Applications | Department of Mathematics

Congratulations for having completed the seven weeks of this course! This module contains the final exam for the course. The exam is cumulative and covers the topics discussed in Weeks The exam has 20 questions and is designed to be a two-hour exam. You have one attempt only, but you do not have to complete the exam within two hours.

Complex variables, simple solutions

The discussion forum will stay open during the exam. It is against the honor code to discuss answers to any exam question on the forum. The forum should only be used to discuss questions on other material or to alert staff of technical issues with the exam. The lectures were very easy to follow and the exercises fitted these lectures well.

This course was not always very rigorous, but a great introduction to complex analysis nevertheless. Thank you! The prof makes it easy to understand yet fascinating.

2nd Edition

I enjoyed video checkpoints, quizzes and peer reviewed assignments. This course encourages you to think and discover new things. Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free. More questions?

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